非齐次树上m重非齐次马氏链的一类强偏差定理

研究给出了非齐次树上m重非齐次马氏链的一类强偏差定理.     

基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

树上非齐次马氏链转移矩阵的若干极限性质

树模型近年来已引起物理学、概率论及信息论界的广泛兴趣.树指标随机过程已成为发展起来的概率论的研究方向.在概率论的发展过程中,对强极限定理的研究一直占重要地位,强极限定理也一直是国际概率论界研究的中心课题之一.本文通过引入样本散度的概念,通过构造适当的非负鞅,将Doob收敛定理应用于几乎处处收敛的研究,给出了非齐次树上m重可列非齐次马氏链转移矩阵的若干极限性质.     

关于可列非齐次马氏链的广义C-强遍历性

马氏链遍历性理论在生物,数值计算,信息理论,自动控制,近代物理和公用事业中的服务系统等众多领域都有着广泛的应用,马氏链的C-强遍历性是马氏链遍历性理论的重要内容.本文给出了马氏链C-强遍历性的一个推广,首先给出了在可列状态空间取值的非齐次马氏链的广义C-强遍历性和广义一致C-强遍历性的概念,然后研究这两种遍历性成立的充分条件.     

EFFECTS OF FINELY DISPERSED METALLIC PALLADIUM ON MICROSTRUCTURE AND PROPERTIES OF NANOCOMPOSITES PRODUCED BY SOL-GEL TECHNIQUE

Nanosized palladium particles were incorporated into mesoporous silica matrix to obtain nanocomposites using the sol-gel technique. Effects of the finely dispersed metallic palladium on the microstructure and properties of the nanocomposites were investigated. By means of X-ray diffraction and optical absorption, it was found that palladium particles were 5-9 nm in diameter and their uniform dispersion in the mesoporous silica depended on both the content of the palladium and the structural features of the silica matrix. The results showed that the mixing method of preparation led to wider size distribution of the nanosized particles as compared to the immersion method, but dispersed degree was reduced. Although the incorporation of nanosized palladium particles could not substantially induce significant structural changes of the matrix, the apparent red-shifted optical absorptions for the nanocomposites were observed as compared to the parent monolithic silica, particularly with increase in palladium loading and calcination temperature.     

DUAL-CHANNEL PARTICLE SIZE AND SHAPE ANALYZER

Fig. 1 shows a newly developed analyzer (Ankersmid CIS-100) that brings together two different measurement channels for accurate size and shape measurement of spherical and non-spherical particles. The size of spherical particles is measured by a HeNe Laser Beam; the size of non-spherical particles is analyzed by Dynamic Video Analysis of the particles‘ shape.     

自紧身管临界裂纹尺寸的概率断裂力学研究

基于概率断裂力学理论和Mome Caflo模拟方法，本文进行了自紧身管临界裂纹尺寸的可靠性研究。自紧身管内表面的疲劳裂纹考虑为半椭圆形式。裂纹尖端处的应力强度因子由内压和自紧残余应力共同产生。自紧残余应力采用了符合身管材料具有强化和包辛格效应性能推导的公式计算，它产生的应力强度因子通过权函数方法得到。根据断裂准则，可计算出自紧身管的临界裂纹尺寸。实例分析表明，对数正态分布为临界裂纹尺寸的最佳分布，同时给出了在各种置信度和可靠度下自紧身管的临界裂纹尺寸。     

Prediction of Quasi-Brittle Fracture of Concrete and Rock Structures Using Laboratory-Sized Specimens

A simple method is developed for predicting the fracture behaviour of struetures made of quasi-brittle materials sueh as eonerete and roek using the data from laboratory-sized speeimens. The method is based on the reeently-developed boundary effeet concept and associated asymptotic model. It is demonstrated that the ＂apparent＂ size dependence of fraeture behaviour of concrete and rock is in fact due to the influence of specimen boundaries. Various size effect phenomena that are often observed in fracture meehanies tests of eoncrete and roek are related to each other, and the asymptotie boundary effect model can explain all the observed ＂size＂ effeet phenomena. Four types of experimental results available in the literature （ineluding the data measured on （1） the speeimens of identical size with different crack-to-size （α） ratios, （2） specimens of different sizes with different a-ratios, （3） different types of specimens and （4） geometrieally similar speeimens） are used to verify the asymptotic boundary effect model, and it is found that the predictions of the model agree very well with the experimental results. Furthermore, the important fracture properties, fracture toughness KIC and strength f, of quasi-brittle materials sueh as eonerete and roek can also be calculated using the formulae provided in the model.     

在同位旋空间中正反质子弹性散射的重整化混合圈链图效应

本文采用描述荷电和中性 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型,计算出在 pion0 重整化混合圈链图传播下 p pbar -> p pbar 弹性散射微分截面的“精确”解析结果;并且将此结果与在 pion0 树图传播下的微分截面作了对比分析,得到相应的辐射修正重要信息。本文完成的工作对进一步深入研究 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型以及深入理论探讨正反质子对撞实验,都将提供理论研究的参考价值。     

突破外形干扰 建构适用模型——由一道考题的分析说起

数学模型,生成于学生的数学认知活动之中,是学生化解新的数学问题的重要工具.在初中阶段,很多数学问题的解决都需要借助已有的数学模型,如相似问题中的"K形图"、二次函数的几种常用解析式等.这些数学模型是学生的数学认知活动的规律总结,在一定范围内具有普遍性和适用性.因此,在教学中,一线老师对模型教学十分关注,他们努力将模型建构在学生获得"四基"的过程之中,让学生不断经历用已有数学模型解决新的